Use WebSocket in .Net6.0

Question

I have a question about how I can also enable the use of WebSocket in my .net6.0 (Project Sdk="Microsoft.NET.Sdk") application

I have a class that creates a broker with logic for processing messages and also depends on other classes

public class MqttBrokerService : IDisposable, IHostedService, IMqttBrokerService
{
  public MqttBrokerService(...)
  {
      var options = new MqttServerOptionsBuilder()
                  .WithDefaultEndpoint()
                  .Build();
  
      _server = new MqttFactory().CreateMqttServer(options);
  }
}

then this class is created in the Program.cs

var webApplicationOptions = new WebApplicationOptions
{
  ContentRootPath = AppContext.BaseDirectory,
  Args = args,
};
var builder = WebApplication.CreateBuilder(webApplicationOptions);
var services = builder.Services;

services.AddHostedService<MqttBrokerService>();

Unfortunately, I don’t understand how else to enable WebSocket support specifically for the broker that will be created in this class

since as far as I understand, only the mqtt server that was created using services can support a connection via a websocket, I also have one more question, how can I create a message in an application where mqtt server is located using another class that should be sent to all subscribed clients? that is, it happens X-Class happen an event and creates a public Task InjectApplicationMessage(InjectedMqttApplicationMessage injectedApplicationMessage) which should be published by this server that was created through the service

I will be very grateful for your help

services.AddSingleton<MqttBrokerService>();
services.AddHostedMqttServerWithServices(options => {
    var s = options.ServiceProvider.GetRequiredService<MqttBrokerService>();
    s.ConfigureMqttServerOptions(options);
});
services.AddMqttConnectionHandler();
services.AddMqttWebSocketServerAdapter();
services.AddConnections();
app.UseRouting();
app.UseEndpoints(
    endpoints =>
    {
        endpoints.MapConnectionHandler<MqttConnectionHandler>(
            "/ws",
            httpConnectionDispatcherOptions => httpConnectionDispatcherOptions.WebSockets.SubProtocolSelector =
                protocolList => protocolList.FirstOrDefault() ?? string.Empty);
        endpoints.MapGet("/", async context =>
        {
            await context.Response.WriteAsync("Hello World!");
        });
    });


app.UseMqttEndpoint();
app.UseMqttServer(server =>
{
    var mqttBrokerService = app.Services.GetRequiredService<MqttBrokerService>();
    mqttBrokerService.ConfigureMqttServer(server);
}); 

I tried to write it like this, but all clients fail ValidatingConnectionAsync, it always fails, and then disconnects, and if this is the only way to look, then how can you add a new message to it through another class that it should publish (not as a client, but as server)